1. Field of the Invention
The present invention relates to a developing apparatus, provided in an image forming apparatus which electrophotographically forms an image, for developing an electrostatic latent image formed on a photosensitive body into a visible toner image, and more particularly to a developing apparatus equipped with a developing roller having a dielectric layer formed on its outer surface.
2. Description of the Related Art
There are known some types of an image forming apparatus that electrophotographically forms an image, employing a developing apparatus for developing an electrostatic latent image formed on the surface of a photosensitive body into a visible toner image by pressing a developing roller having a toner layer formed on its outer surface against the surface of the photosensitive body by a predetermined nip width during the developing process. There is known a developing roller provided in such a developing apparatus, including conductive elastic rubber of high resistance as its outer surface. However, an elastic material of high resistance exhibits considerable variations in resistance value, and an error in resistance value may occur among different developing rollers and among different portions in a single developing roller. Also, a variation in resistance value readily occurs with an external environment such as humidity.
Hence, there is known a dielectric developing roller for a conventional developing apparatus directed to stabilization of resistance value, comprising a conductive substrate, and a resistance layer and a dielectric layer which are formed on the outer surface of the conductive substrate in this order.
Japanese Unexamined Patent Publication JP-A 1-230079 (1989) discloses a monocomponent developing apparatus using a developing roller having at least a dielectric layer deposited on the top surface of a supporting layer made of an elastic material, wherein, based on a saturation development model of a capacitor type, resistance of the supporting layer is set lower than a value determined by a bias potential, an amount of charge of toner, etc.
Japanese Unexamined Patent Publication JP-A 3-87759 (1991) discloses a developing method of readily obtaining a sharp and uniform image of high density without any fog on the background by adjusting the following: an amount of charge of toner adhering to a surface holding an electrostatic latent image as a result of development; an amount of charge conferred to toner through frictional electrification with the surface holding the electrostatic latent image; an electric resistance value of a toner carrier; an effective length of the toner carrier; an effective area of the toner carrier; an amount of adhesion of toner on the surface holding the electrostatic latent image as a result of development; a moving rate of the surface holding the electrostatic latent image; an amount of adhesion of toner on the surface of the toner carrier; and a speed ratio between the surface of the toner carrier and the surface holding the electrostatic latent image.
However, none of the conventional dielectric developing rollers is arranged to upgrade an image quality during the image formation by making it easier to set developing conditions that exert influence upon a developing state during the developing process, including: a thickness and a dielectric constant of a photosensitive layer of the photosensitive body; a thickness, a dielectric constant, and an amount of adhesion per unit area of a toner layer formed on the developing roller; a thickness and a dielectric constant of the dielectric layer of the developing roller; a thickness, a dielectric constant, and specific resistance of the resistance layer of the developing roller; a potential of a non-exposure region and an exposure saturation potential both on the photosensitive body before entering into a developing portion; a specific charge of the toner before entering into the developing portion; a nip width of the developing portion; a peripheral speed ratio of the photosensitive body and developing roller; etc. Hence, the design of the apparatus becomes complicated, which results in a problem that the cost is undesirably increased.
Neither JP-A 1-230079 nor JP-A 3-87759 supra discloses an equation indicating the developing conditions using each of the foregoing parameters.
It is therefore an object of the invention to provide a developing apparatus provided with a dielectric developing roller, in which optimal developing conditions to upgrade an image quality during image formation can be readily set, thereby making it possible to achieve cost reduction by facilitating the design of the apparatus.
The invention has the following arrangements as means to solve the problems discussed above.
The invention provides a developing apparatus for developing an electrostatic. latent image into a toner image, comprising:
a developing roller including a conductive substrate, and a resistance layer and a dielectric layer which are formed on a surface of the conductive substrate,
the developing apparatus developing at a developing portion where the developing roller contacts a photosensitive body including a conductive substrate and a photosensitive layer formed on a surface of the conductive substrate, by a predetermined nip width, an electrostatic latent image formed on the photosensitive layer into a toner image by layered toner carried on a peripheral surface of the developing roller,
wherein a relation expressed by the following Equation (1) is established:
Ccxe2x89xa7xcfx81txc2x7dtxc2x7k/Vvxe2x80x83xe2x80x83(1)
wherein
Vv=xe2x88x92(Vbp+Vpr)xe2x88x92Vco+Vtxc2x7k
Cc=1/{1/Cp+2/Ct+rr/k+1/(Cr3xc2x7k)}
k=vr/vp
rr=xcfx81rxc2x7d2
Cp=∈p/dp
Ct=2∈t/dt
Cr1=∈1/d1
Cr2=∈2/d2
C1=1/{1/Cp+2/Ct+1/(Cr1xc2x7k)}
C2=kxc2x7Cr2
Ex=(W/vp)/{rrxc2x7(C1+C2)}
Cr3=Cr1xc2x7{1xe2x88x92C1/(C1+C2)}xc2x7exp(xe2x88x92Ex)
xcfx81t=(qpm+qr)xc2x7m/dt
Vco=xe2x88x92qpmxc2x7m/Cr1
Vpr=xe2x88x92qrxc2x7mxc2x7k/Cp
Vt=xcfx81txc2x7dt/Ct,
wherein dp (m) and sp (F/m) are thickness and dielectric constant of the photosensitive layer of the photosensitive body, respectively, dt (m), ∈t (F/m) and m (kg/m2) are thickness, dielectric constant and amount of adhesion per unit area of a toner layer formed on the photosensitive body, respectively, d1 (m) and ∈1 (F/m) are thickness and dielectric constant of the dielectric layer of the developing roller, respectively, d2 (m), ∈2 (F/m) and xcfx81r (xcexa9xc2x7m) are thickness, dielectric constant, specific constant of the resistance layer of the developing roller, respectively, Vbp (=Vsxe2x88x92Vb) (V) is potential difference between photosensitive body surface potential Vs (V) in a saturation image density region on the photosensitive body before entering into the developing portion and developing bias Vb (V), qpm (C/kg) is specific charge of toner before entering into the developing portion, Vco (V) is voltage of the dielectric layer of the developing roller before entering into the developing portion, qr (C/kg) is amount of change in specific charge of the toner caused by passing through the developing portion, W (m) is nip width of the developing portion, vp (m/s) is peripheral speed of the photosensitive body, and vr (m/s) is peripheral speed of the developing roller.
In the invention, the developing conditions that exert influence upon a developing state during the developing process, including: the thickness and dielectric constant of the photosensitive layer of the photosensitive body; the thickness, dielectric constant and amount of adhesion per unit area of the toner layer formed on the developing roller; the thickness and dielectric constant of the dielectric layer of the developing roller; the thickness, dielectric constant and specific resistance of the resistance layer of the developing roller; a potential of a non-exposure region and an exposure saturation potential both on the photosensitive body before entering into the developing portion; the specific charge of toner before entering into the developing portion; the nip width of the developing portion; and the peripheral speed ratio of the photosensitive body and the developing roller, are set so as to satisfy Equation (1). Equation (1) is a conditional expression to attain developing efficiency of 100%, at which the layer of toner carried on the outer surface of the developing roller is allowed to migrate entirely to the photosensitive body. Hence, when each developing condition satisfies Equation (1) above, toner migrates from the developing roller to the photosensitive body in a reliable manner, thereby enhancing the developing efficiency.
According to the invention, by setting the developing conditions that exert influence upon the developing state during the developing process, including: the thickness and dielectric constant of the photosensitive layer of the photosensitive body; the thickness, dielectric constant and amount of adhesion per unit area of the toner layer formed on the developing roller; the thickness and dielectric constant of the dielectric layer of the developing roller; the thickness, dielectric constant, and specific resistance of the resistance layer of the developing roller; the potential of the non-exposure region and the exposure saturation potential both on the photosensitive body before entering into the developing portion; the specific charge of toner before entering into the developing portion; the nip width of the developing portion; and the peripheral speed ratio of the photosensitive body and developing roller, so as to satisfy the relation expresses as Ccxe2x89xa7xcfx81txc2x7dtxc2x7k/Vv, it is possible to allow the toner to migrate from the developing roller to the photosensitive body in a reliable manner, and therefore, to achieve a satisfactory image density by enhancing the developing efficiency.
The invention is characterized in that Equation (1) is modified to:
Ccxe2x89xa7xcfx81txc2x7dtxc2x7k/(Voxe2x88x92V1),
wherein Vo is potential in a non-exposure region of the photosensitive body and V1 (V) is exposure saturation potential on the photosensitive body before entering -into the developing portion.
In the invention, the developing conditions are set based on the conditional expression with consideration given to a potential difference between the potential of the non-exposure region and the exposure saturation potential of the exposure region both on the photosensitive body before entering into the developing portion. This allows to secure satisfactory developing efficiency within an effective developing potential width representing a potential difference between the non-exposure region and exposure region on the photosensitive body, thereby inhibiting the occurrence of a fog of an image even when an image density is high.
The invention is characterized in that Equation (1) is modified to:
Ccxe2x89xa7xcfx81txc2x7dtxc2x7k/{Voxe2x88x92V1xe2x88x92Vmxc2x7Sign(Vo)
wherein Sign(n)=1, Sign(xe2x88x92n)=xe2x88x921 when n greater than 0, and Vm (V) is operation margin.
In the invention, the developing conditions are set based on the conditional expression with consideration given to the operation margin with respect to the effective developing potential width. Hence, even when a developing potential varies with a difference among individual apparatuses, an environmental change, etc., it is possible to secure satisfactory developing efficiency within the effective developing potential width.
In the invention, it is preferable to set Vm=100 (V)
According to the invention, satisfactory developing efficiency can be secured within a predetermined effective developing potential width, thereby making it possible to prevent a fog of an image without impairing tone reproduction of the image.
The invention is characterized in that Equation (1) is modified to:
Ccxe2x89xa6xcfx81txc2x7dtxc2x7k/(Vo/3).
In the invention, the developing conditions are set so that satisfactory developing efficiency can be secured within ⅓ the region of-the potential of the non-exposure region on the photosensitive body before entering into the developing portion. This allows adjustment of the developing efficiency within at least ⅓ the region of the photosensitive body potential, thereby making it possible to render satisfactory tone reproduction on an image.
The invention is characterized in that:
(W/vp) greater than {rrxc2x7(C1+C2)}.
In the invention, deterioration in response caused by a time constant of an electric circuit formed at the developing portion can be prevented. Hence, it is possible to prevent inconveniences such that an image is not formed due to deterioration in response.
According to the invention, by setting the developing conditions so as to prevent deterioration in response caused by a time constant of the electric circuit formed at the developing portion, it is possible to prevent inconveniences such that an image is not formed due to deterioration in response.
The invention is characterized in that:
xe2x80x831/Cp+2/Ct+rr/kxe2x89xa74/(Cr3xc2x7k).
In the invention, deterioration in response caused by a time constant of the electric circuit formed at the developing portion is controlled to fall within20%. Thus, the developing efficiency never drops to 80% or below by deterioration in response, thereby making it possible to maintain a satisfactory image forming state.